How does an electricity meter add up energy use?

A powerful appliance running briefly can use less energy than a modest appliance left running for hours. An electricity meter captures that difference. It does not merely remember the largest power reading or count how many devices are switched on. It accumulates the electrical energy transferred over time, keeping a running total even as a home's demand rises and falls.

Power is the rate of energy transfer: one watt means one joule each second. Energy is the amount transferred. The difference resembles water flowing into a tank: flow rate describes how quickly water arrives, while the accumulated volume depends on how long that flow continues. For constant power, energy equals power multiplied by duration. Multiplying watts by hours gives watt-hours, or Wh. A kilowatt-hour is 1,000 Wh, equivalent to 3.6 million joules.

An electronic meter measures voltage and current repeatedly. Multiplying simultaneous voltage and current values gives instantaneous power; accumulating these power contributions over time gives energy. This timing matters with alternating current because voltage and current vary through each cycle and need not rise and fall together. Multiplying separate average magnitudes is not generally enough. The meter's job is to keep track of the actual energy transfer represented by their changing product.

Consider an invented four-hour record: 100 watts for the first two hours, 300 watts for the next hour, then zero for the last hour. The first interval adds 200 Wh; the second adds 300 Wh; the last adds nothing. The total increase is 500 Wh, or 0.5 kWh. The meter's existing reading would increase by that amount. Switching everything off would stop further accumulation in this example, not erase the energy already recorded.

On a graph of power against time, each constant-power interval forms a rectangle. Its height is power and its width is duration, so its area is energy. Adding the areas gives the same 500 Wh. For smoothly changing power, this becomes the integral E = ∫ P(t) dt. A cumulative-energy graph tells the story another way: its height is the energy accumulated so far, and its slope is power. It rises gently at 100 W, more steeply at 300 W, then becomes flat at zero.

Over all four hours, average power is 500 Wh divided by 4 h, or 125 W. Simply averaging 100, 300 and 0 would give the wrong result because those levels lasted different lengths of time. Duration is part of the evidence. The meter is doing a quiet piece of mathematics every day: turning a changing rate into an accumulated amount. The same relationship connects speed with distance and water flow with reservoir volume.